3 problems

Let $S$ be a closed surface with fundamental group $\Gamma$, let $d\geq 2$, and let $\lambda$ be a maximal geodesic lamination on $S$. Denote by $\mathfrak R(\lambda,d)$ the space…

Let $\Sigma$ be a closed surface of genus at least two, and let a hyperbolic convex core structure on $\Sigma\times[0,1]$ be a hyperbolic structure whose developing map is a homeom…

Let $M$ be a geometrically finite hyperbolic 3-manifold. The boundary of its convex core carries an induced path metric that is locally hyperbolic and is bent along a geodesic lami…